Potentials, E B drifts, and uctuations in the DIII-D boundary

Journal of Nuclear Materials 266±269 (1999) 1145±1150 Potentials, E B drifts, and uctuations in the DIII-D boundary R.A. Moyer a, *, R. Lehmer a, J.A. Boedo a, J.G. Watkins b,x.xu c, J.R. Myra d, R. Cohen c, D.A. D'Ippolito d, T.W. Petrie e, M.J. Scha er e a Fusion Energy Research Program, University of California, San Diego, La Jolla, CA 92093-0417, USA b Sandia National Laboratories, Albuquerque, NM 87185, USA c Lawrence Livermore National Laboratory, Livermore, CA 94551, USA d Lodestar Research Corporation, Boulder, CO 80301, USA e General Atomics, P.O. Box 85608, San Diego, CA 92186-5688, USA Abstract Reciprocating Langmuir probes are used to investigate the structure of electrostatic potentials, E B drifts, and uctuations in the edge (q < 1), scrape-o layer (SOL) and divertor of single null diverted discharges in the DIII-D tokamak. These measurements demonstrate that the X-point geometry suppresses potential uctuations in the drift wave range of frequencies (20 khz 6 f 6 300 khz) as predicted by theory [N. Mattor and R.N. Cohen, Phys. Plasmas 2 (1995) 4042], and suppresses quasi-coherent modes in the edge of H-modes. Consequently, edge turbulence and ballooning mode stability calculations, such as those used in L±H transition and H mode pedestal theories, must incorporate realistic X-point magnetic geometry to quantitatively reproduce experimental results. In the divertor plasma, root-mean-square potential uctuations ~ /, are found to be larger in H mode than in L mode, and in detached versus attached divertor plasmas. These measurements have been used to benchmark turbulence simulations with two unique codes that incorporate realistic X-point magnetic geometry: the 3-D boundary turbulence code BOUT and the BAL shooting code with high-n ballooning formalism. Ó 1999 Elsevier Science B.V. All rights reserved. Keywords: Fluctuations; X-point; Plasma edge physics; Scrape-o layer; DIII-D 1. Introduction Despite several decades of research, our understanding of edge turbulence and transport remains incomplete. For example, the unstable modes, drives and dissipation mechanisms have not yet been conclusively identi ed [1]. In addition, the e ects of conditions such as neutral pressure, radiation, and magnetic shear are not yet completely understood. Signi cant progress has nonetheless been possible due to the generality of the E B shear suppression mechanism, which permits turbulent transport to be controlled without the need to * Corresponding author. Tel.: +1 619 455 2275; fax: +1 619 455 4156; e-mail: moyer@gav.gat.com. identify the underlying modes or drives. Recent theoretical work has focused on the complex issues associated with coupling of the core to the SOL across the H- mode pedestal region, including the e ects of neutral pressure [2], neoclassical SOL currents [3], and edge microturbulence [4±7]. Systematic study of the plasma pro les and uctuations in the boundary is needed to test these increasingly more complex theories. In this paper, we present measurements of electron pressure P e ˆ n e KT e, plasma / pl potential pro les and potential uctuations / ~ at three poloidal locations in the DIII-D tokamak: the outboard midplane, the lower divertor, and the bottom of upper single null discharges ± analogous to the `top' of lower single null divertor plasmas, as shown in Fig. 1. Measurements are obtained with two reciprocating Langmuir probe arrays [8,9] capable of scanning the SOL/ and d.c. oating / dc 0022-3115/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2-3 1 1 5 ( 9 8 ) 0 0 6 1 8-7

1146 R.A. Moyer et al. / Journal of Nuclear Materials 266±269 (1999) 1145±1150 Fig. 1. Equilibrium ux surface reconstructions from EFIT for the (a) lower single null and (b) upper single null divertor discharges in this work. The midplane and X-point probe locations are indicated by the horizontal and vertical bars respectively. The R sep and Z sep values are the locations of the separatrix in the probe path for the midplane probe (Z probe ˆ 0.19 m) and X-point probe (R probe ˆ 1.488 m) respectively. divertor plasma up to and just inside the separatrix. The probe array in the lower divertor, the `X-point probe', provides simultaneous measurements of n e and T e, the main ion ows parallel to the magnetic eld [10], and the d.c. and uctuating oating potential / dc and / ~. These measurements are compared with the same quantities measured simultaneously at the outboard midplane and with the results of simulations using the BOUT 3-D boundary turbulence code [11] and of calculations using the BAL shooting code with high-n ballooning formalism [12]. These codes have the unique capability to handle realistic X-point magnetic geometry, which is critical for reproducing the experimental results. 2. Poloidal variation of potential uctuations Data have been acquired in two sets of single null divertor L mode discharges: lower and upper single null. Signi cant changes to the inside of the DIII-D vessel, including installation of the upper outer divertor ba e plate and cryopump [13], occurred between the time that the lower and upper single null data were acquired. To account for these variations, the data from the lower divertor chamber are compared against simultaneous outboard midplane measurements in each case. Typical measurements in the SOL at the `top' of the discharge (a) and in the vicinity of the X-point (b) are shown in Fig. 2. In Fig. 2(a), the electron pressure P e pro le at the `top' () is similar in shape to the midplane pro le (D), indicating that P e is nearly poloidally symmetric, to within the uncertainty in the ux surface mapping. Both Fig. 2. Pro les of local plasma and potential uctuation parameters versus normalized poloidal ux coordinate W n for L mode discharges with (a) upper single null and (b) lower single null divertors. In (a) the X-point probe scans a region equivalent to the `top' () of a lower single null discharge. In (b) the X- point probe scans the lower divertor private ux () and the outer SOL and X-point ( ) regions. The pro les are, from top to bottom: electron pressure P e, plasma potential / pl, absolute rms potential uctuation level ~ /, and normalized rms potential uctuation level ~ /=T e. the plasma potential / pl and the rms potential uctuation amplitude ~ / map well from the `top' to the outboard midplane. T e pro le di erences lead to a reduction in the normalized rms amplitude from 30% on the outboard midplane to 20% at the `top'. For the set of discharges in Fig. 2(b), the X-point was located just inboard of the vertical stroke of the X-point probe, pro-

R.A. Moyer et al. / Journal of Nuclear Materials 266±269 (1999) 1145±1150 1147 viding access to the X-point vicinity but limiting the amount of data obtained in the outer SOL [Fig. 1(a)]. The data in the outer SOL and plasma core ( ) near the X-point cover a limited range in the normalized poloidal ux coordinate W n : 0.998 6 W n 6 1.002, although the spatial extent is 5 cm (outer SOL) and 4 cm (core); see Fig. 5. Near the X-point, the local P e and / pl have strong poloidal variations which complicate comparisons with the midplane measurements. However, it is clear that: (1) P e near the X-point exceeds the midplane value, (2) a strong gradient in / pl exists across the separatrix between the private ux and SOL regions [14], and (3) the rms amplitude / ~ is a factor of 2 or more lower near the X-point than on the same W n surface at the outboard midplane. These conclusions are con rmed by analysis of the potential uctuations at a xed W n in the frequency domain, as shown in Fig. 3. In Fig. 3(a), the potential autopower spectrum P // (x) (proportional to / ~ 2 ) at the ``top'' of the plasma near the separatrix (W n ˆ 1.01 corresponding to 0.5 cm outside the separatrix on the outboard midplane) is comparable to the midplane spectrum across the frequency range associated with the turbulent particle transport C(x). In contrast, P // (x) near the X-point [Fig. 3(b)] is substantially reduced in the frequency range 20 6 f 6 300 khz where most of the turbulent particle transport C(x) occurs. Similar results are obtained up to W n ˆ 1.01 into the SOL (2 cm in e ective midplane radius). Together, these measurements indicate that electrostatic uctuations due to E B drift wave like modes in the frequency range 20 khz 6 f 6 300 khz are suppressed in the vicinity of the X-point, as predicted by Mattor et al. [15]. In Fig. 4(a), P // (x) on the outboard midplane is compared to P // (x) near the X-point in a ELM-free H- mode phase. The L-mode spectrum is also shown for reference. These spectra show that the rms amplitude ~ / obtained by integrating P // (x) over x is larger near the X-point in H-mode than in L-mode due to an increase in P // (x) in the drift wave range of frequencies that were strongly suppressed in L-mode. However, P // (x) at the X-point remains lower than the midplane value in the drift wave range of frequencies due to the lack of strong quasi-coherent mode activity which is seen just inside the separatrix at the midplane in these H-modes. In Fig. 4(b), the autocorrelation functions corresponding to the H-mode midplane and X-point power spectra in Fig. 4(a) are compared. The midplane potential autocorrelation function shows a clear signature of strong coherent activity (the periodic oscillations in the wings of the autocorrelation function), while this feature is far less pronounced (but not completely absent) in the X- point data. These measurements indicate the quasi-coherent mode, which dominates the potential (and density, not shown here) power spectra at the midplane, is also greatly suppressed near the X-point. 3. Divertor potentials and uctuations: L versus H mode Although it is common to measure uctuation suppression right after the L±H transition, uctuations can Fig. 3. Comparison of potential uctuation autopower spectra P // (x) for (a) the `top' and midplane at W n ˆ 1.01, and (b) the X-point vicinity and midplane at W n ˆ 0.998 in single null divertor L mode discharges. The frequency resolved turbulent particle ux C(x) is shown to indicate the frequency range where most of the particle transport is driven (shaded regions). Due to uncertainties in mapping the data to a common W n value, power spectra from neighboring W n (a) at the `top' of the machine and (b) at the outboard midplane are provided to demonstrate that the conclusions are insensitive to the mapping uncertainties.

1148 R.A. Moyer et al. / Journal of Nuclear Materials 266±269 (1999) 1145±1150 Fig. 4. (a) Comparison of potential uctuation autopower spectra P // (x) near the X-point () and at the outboard midplane (h) in an ELM-free H-mode. The L mode P // (x) (m) is shown for comparison. The frequency range for turbulent particle transport is shaded. (b) Comparison of the potential autocorrelation functions near the X-point and on the outboard midplane. The data for (a) and (b) are both from W n ˆ 0.998. rise inside the E r shear layer/h-mode pedestal region in established H-modes due to increased turbulence drive, particularly for potential uctuations [16]. In Fig. 5, changes in the vicinity of the X-point between established L and ELM-free H-modes (just prior to ELM onset) are shown. Although the local density is essentially unchanged, T e rises signi cantly in both the outer SOL and in the core near the X-point. There is a corresponding drop to a more negative / dc. The rms potential uctuations / ~ dc, however, are a factor of 2 higher across the outer leg of the divertor and into the core near the X-point in H-mode. This measurement contrasts with measurements at the outboard midplane, where the electrostatic uctuation amplitudes are higher only inside the separatrix, not in the SOL [16]. The result is that the normalized rms amplitude remains nearly constant, although there is considerably more `jitter' at low frequency [f 6 10 khz; Fig. 4(a)] in the L-mode phase. This jitter may be related to the fact that most low power L- modes, like those reported here, are either partially or fully detached in DIII-D. Fig. 5. Variation of plasma and potential uctuation parameters versus height above the divertor target in established () L and (n) ELM-free H-mode phases of identical discharges in DIII-D. The regions where the X-point probe is traversing the private ux, outer SOL, and core regions are indicated. The parameters are, from top to bottom: electron density n e, electron temperature T e, d.c. oating potential / dc, absolute rms potential uctuation level / ~, and normalized rms potential uctuation level /=T ~ e. 4. Potentials and ucutations in detached divertor plasmas In Fig. 6(a), we compare the divertor conditions for attached () and detached (n), slowly ELMing H-mode discharges. For these probe plunges, the outer strike point was over the penetration in the divertor oor for the probe, and the probe traveled nearly within a ux surface, yielding pro les that rise rapidly to the maximum value and remain nearly constant thereafter. Consistent with detachment, n e is 2±4 higher and T e 2± 3 lower in the outer leg of the divertor. Note that in detached plasmas, the swept double probe yields values

R.A. Moyer et al. / Journal of Nuclear Materials 266±269 (1999) 1145±1150 1149 Fig. 6. (a) Variation of plasma and potential uctuation parameters versus height above the divertor target in established, slowly ELMing H-modes with () attached and (D) detached outer divertor leg plasmas. The parameters are, from top to bottom: electron density n e, electron temperature T e, d.c. oating potential / dc, absolute rms potential uctuation level / ~, and normalized rms potential uctuation level /=T ~ e. Note the logorithmic y axis for the plot /=T ~ e. (b) Potential uctuation autopower spectra P // (x) in slowly ELMing (top; t ˆ 2700 ms) and rapidly ELMing (bottom; t ˆ 3700 ms) with (solid) attached and (dashed) detached outer divertor leg plasmas. The region below about 16 khz where P // (x) is strongly enhanced during detachment is indicated by the shaded areas. for T e that are systematically 2±3 times higher than T e from divertor Thomson scattering [17] so that the values of /=T ~ e reported here for detached plasmas are lower bounds. This di erence arises primarily due to the distortion of the probe I±V characteristics by the large amplitude, low frequency (1 khz 6 f 6 15 khz) uctuations [10] which are strongly enhanced in detached divertor plasmas, as shown in Fig. 6(b). Note also that attached plasmas generally have / dc < 0 [Fig. 5(a); Fig. 6(a)]. When the divertor detaches, the oating potential rises above 0, but is transiently carried negative during each ELM. This behavior suggests that some ELMs transiently reattach the divertor plasma. It was previously reported [17] that ELMs transiently enhanced ~/=T e by a factor of 2 in attached divertors, and a factor of 2±10 in detached divertors. In Fig. 6(a), it is clear that the rms amplitude / ~ is increased a factor of 2 in detachment even between the slow ELMs. Combined with the decrease in T e, this leads to an increase in the normalized amplitude /=T ~ e by a factor 2±4 between ELMs, and much more during the ELMs [note the logorithmic scale in Fig. 6(a)]. Later in these discharges, the neutral beam power was increased to produce rapidly ELMing H-modes. Similar results were obtained in those rapidly ELMing phases. 5. Discussion The data presented here have been used to `benchmark' simulations of the boundary (edge and SOL) turbulence [11] with the BOUT code [18]. The BOUT code simulates E B drift resistive ballooning-like modes in realistic DIII-D magnetic geometry. The code has, for turbulence codes, the unique ability to model the X-point geometry properly. For the discharges presented here, the BOUT code calculates that the broadband turbulence is due to drift resistive ballooning-like modes with toroidal mode number n between 200 and 400. The resulting density uctuation power spectra and frequency resolved particle ux C(x) are qualitatively consistent with the spectra measured at the outboard midplane, including a signi cant range of f 1 dependence [11]. The BOUT simulations also show that the

1150 R.A. Moyer et al. / Journal of Nuclear Materials 266±269 (1999) 1145±1150 unstable modes associated with the turbulence do not extend into the X-point region, consistent with the experimental data. Myra et al. have modeled the appearance of a strong quasi-coherent feature in the ELM-free H-mode with BAL, a shooting code with high-n ballooning formalism [12], which also incorporates the X-point magnetic geometry. Using the high-n ballooning formalism, the code nds modes that are robustly unstable for n < 50 and are near the ideal MHD stability boundary. The code yields instability for this class of modes only in the H- phase of the discharge. The corresponding eigenmodes balloon in the bad curvature region and are small in the X-point and divertor region [19]. These calculations are consistent with the experimental observations in Section 2. Watkins et al. have determined that the probability distribution for T e at the target plates in detached divertor plasmas is strongly skewed from a low of 1±2 ev to 10 ev due to the presence of energetic electrons in the pulse associated with the ELM [20]. Such an energetic (nonthermal) electron pulse would e ect on the oating potential measurements, driving the d.c. potential negative as observed during the ELMs. While this observaton explains the large excursions in / dc and /=T ~ e during the ELMs, it does not explain the large normalized uctuation amplitudes /=T ~ e in L-mode and between ELMs in detached H-mode conditions. In these detached divertor plasmas, the X-point region is dynamically very active, appearing to `` icker'' between a detached state and an attached state spontaneously triggered by the ELM heat and/or energetic electron pulses burning through the radiating zone. 6. Summary Electrostatic uctuations in the DIII-D boundary are found to be suppressed in the vicinity of the X-point relative to both the outboard midplane and the `top' of the SOL. Strong quasi-coherent mode activity inside the separatrix in H-modes (inside the E r shear layer) is also strongly suppressed near the X-point. These observations are consistent with modeling of the broadband turbulence (BOUT) and the quasi-coherent modes (BAL) in the full X-point geometry. These results stress the importance of incorporating realistic magnetic geometry into turbulence and MHD stability codes such as those routinely used to evaluate L±H transition models [7]. The rms uctuation amplitude / ~ in the divertor increases in H mode relative to L mode due to a broadening of the uctuation power spectrum. The spectral broadening raises the mean frequency above the 5±10 khz typically seen in L mode divertor plasmas to values closer to those at the midplane and top of the SOL. The low mean frequency and narrow power spectra in L mode are similar to those in detached, ELMing H-mode discharges, most likely due to the tendency of low power L modes like those studied here to be partially or fully detached in DIII-D. The low frequency uctuations lie outside the frequency range of E B drift wave-like modes where most of the anomolous perpendicular transport occurs, and are quite di erent in character from broadband turbulence (e.g. ~/=T e and ~ /=/ > 1). The data present a picture of the X- point region of detached diverted discharges as dynamically very active, in contrast to having a well-de ned ``equilibrium'' about which there are relatively small turbulent oscillations. Acknowledgements Work supported by US Department of Energy under Grant DE-FG03-95ER54294, and Contract Nos. DE- AC03-89ER51114, W-7405-ENG-48, DE-FG02-97ER54392 and DE-AC04-95AL85000. References [1] B.A. Carreras, IEEE Trans. on Plasma Science 25 (1997) 1281. [2] L.W. Owen et al., Plasma Phys. Control Fusion 40 (1998) 717. [3] F.L. Hinton, G.M. Staebler, Nucl. Fusion 29 (1989) 405. [4] J.G. Cordey, W. Kerner, O. Pogutse, Plasma Phys. Control. Fusion 37 (1995) 773. [5] R.H. Cohen, X.Q. Xu, Phys. Plasmas 2 (1995) 3374. [6] J.G. Cordey et al., Plasma Phys. Control. Fusion 38 (1996) 1905. [7] B. Rogers, J.F. Drake, Phys. Rev. Lett., submitted. [8] J.G. Watkins et al., Rev. Sci. Instrum. 63 (1992) 4728. [9] J.G. Watkins et al., Rev. Sci. Instrum. 68 (1996) 373. [10] J.A. Boedo et al., these Proceedings. [11] X.Q. Xu et al., these Proceedings. [12] J.R. Myra, D.A. D'Ippolito, J.P. Goedbloed, Phys. Plasmas 4 (1997) 1330. [13] S.L. Allen et al., these proceedings. [14] J.A. Boedo et al., Plasma Flow in the DIII-D Divertor in 25th European Physical Society Conference on Controlled Fusion and Plasma Physics 1998, European Physical Society, Czech Republic, Prague. [15] N. Mattor, R.N. Cohen, Phys. Plasmas 2 (1995) 4042. [16] R.A. Moyer et al., Phy. Plasmas 2 (1995) 2397. [17] R.A. Moyer et al., J. Nucl. Mater. 241-243 (1996) 633. [18] X.Q. Xu, R.H. Cohen, Contributions to Plasma Physics 36 (1996) 202. [19] J.R. Myra et al., In 1998 International Sherwood Theory Conference 1998, Atlanta, Georgia. [20] J.G. Watkins et al., these Proceedings.